You create a server by calling
:server t. The server will listen for connection requests from
clients. When it accepts a client connection request, that creates a
new network connection, itself a process object, with the following
nil, the connection process does not get a separate process buffer; otherwise, Emacs creates a new buffer for the purpose. The buffer name is the server's buffer name or process name, concatenated with the client identification string.
The server's process buffer value is never used directly by Emacs, but it is passed to the log function, which can log connections by inserting text there.